Problem: Express this quotient in scientific notation: ${\frac{3.120\times 10^{2}} {4.0\times 10^{0}}}$
Answer: Start by collecting like terms together. $= {\frac{3.120} {4.0}} \times{\frac{10^{2}} {10^{0}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.78 \times 10^{2\,-\,0}$ $= 0.78 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.78$ is the same as $7.80 \div 10$ , or $7.80 \times 10^{-1}$ $ = {7.80 \times 10^{-1}} \times 10^{2} $ $= 7.80\times 10^{1}$